Concrete Strength An engineer wants to know if the mean strengths of three different concrete mix designs differ significantly. He also suspects that slump may be a predictor of concrete strength. Slump is a measure of the uniformity of the concrete, with a higher slump indicating a less uniform mixture. The following data represent the 28-day strength (in pounds per square inch) of three different mixtures with three different slumps.

(a) Normal probability plots indicate that it is reasonable to believe that the data come from populations that are normally distributed. Verify the requirement of equal population variances.

(b) Determine whether there is significant interaction between mixture type and slump.

(c) If there is no significant interaction, determine whether there is significant difference in the means for the three types of mixture. If there is no significant interaction, determine whether there is significant difference in the means for the slumps.

(d) Draw an interaction plot of the data to support the results of parts (b) and (c).

(e) The residuals are normally distributed. Verify this.

(f) If there is significant difference in the means for the three mixture types, use Tukey’s test to determine which pairwise means differ using a familywise error rate of . If there is significant difference in the means for the slumps, use Tukey’s test to determine which pairwise means differ using a familywise error rate of .

Breakeven analysis is one of the simplest yet underused analytical tools in management. It helps provide a dynamic view of the relationships among sales, costs, and profits. A better understanding of breakeven analysis can enable an organization to formulate and implement strategies more effectively. This exercise will show you how to calculate breakeven points mathematically. The formula for calculating breakeven point is BE Quantity = TFC/P – VC. In other words, the quantity (Q) or units of product that need to be sold for a firm to break even is total fixed costs (TFC) divided by (Price per Unit – Variable Costs per Unit). Instructions Step 1 Assume an airplane company has fixed costs of $100 million and variable costs per unit of $2 million. The planes sell for $3 million each. What is the company’s breakeven point in terms of the number of planes that need to be sold just to break even? Step 2 If the airplane company wants to make a profit of $99 million annually, how many planes will it have to sell? Step 3 If the company can sell 200 airplanes in a year, how much annual profit will the firm make?